Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
r,c = map(int,raw_input().split())
e = 0
e1 = 0
rr = []
cc = []
flag = 0
f = [map(int,raw_input().split()) for _ in xrange(r)]
if r>c:
	f=map(list,zip(*f))
	flag =1
	r,c=c,r
for i in xrange(r):
	b = f[i]
	b1 = min(b)
	for j in xrange(c):
		b[j]= b[j]-b1
	f.append(b)
	for w in xrange(b1):
		e+=1
		rr.append(i+1)
f=map(list,zip(*f))
#print f
for i,_ in enumerate(f):
	if min(_)==max(_):
		for j in xrange(min(_)):
			e+=1
			cc.append(i+1)
	else:
		e1=1
		break
if e1==1:
	print -1
else:
	if e==0:
		print 0
	else:
		print e
		if flag ==0:
			for i in rr:
				print 'row %i'%i
			for i in cc:
				print 'col %i'%i
		else:
			for i in cc:
				print 'row %i'%i
			for i in rr:
				print 'col %i'%i